Dipolar quantum electrodynamics of the two-dimensional electron gas

Abstract

Similarly to a previous work on the homogeneous electron gas [Y. Todorov, Phys. Rev. B 89, 075115 (2014)], we apply the Power-Zienau-Wooley (PZW) formulation of the quantum electrodynamics to the case of an electron gas quantum confined by one-dimensional potential. We provide a microscopic description of all collective plasmon modes of the gas, oscillating both along and perpendicular to the direction of quantum confinement. Furthermore, we study the interaction of the collective modes with a photonic structure, planar metallic waveguide, by using the full expansion of the electromagnetic field into normal modes. We show how the boundary conditions for the electromagnetic field influence both the transverse light-matter coupling and the longitudinal particleparticle interactions. The PZW descriptions appear thus as a convenient tool to study semiconductor quantum optics in geometries where quantum-confined particles interact with strongly confined electromagnetic fields in microresonators, such as the ones used to achieve the ultrastrong light-matter coupling regime.

Breakdown of gauge invariance in ultrastrong-coupling cavity QED

“…Instead, in the case of intersubband polaritons, both theories based on the Coulomb [14,85] and on the electric dipole [22,79,86] gauges have been used. The two approaches led to slightly different predictions, which, however, cannot be trivially interpreted in the light of the present results due to their more microscopic nature, which includes the intrinsically multi-mode nature of the photonic cavity and a different treatment of dipoledipole interactions.…”

Quantizing polaritons in inhomogeneous dissipative systems

“…However as we will show in the next subsection the lossless idealization represents a good approximation for a quite general class of medium with weak dissipation. The previous results of Hopfield and Fano have still a physical meaning and are for example used with success for the description of planar cavity polaritons [30,[93][94][95][96][97][98].…”

Hedin equations in resonant microcavities

“…1. In this framework, the Bethe-Salpeter equations (13) and (15) 2. The formal structure of these non-relativistic QED Hedin's equations is analogous to two cases already studied in the literature: The first is the relativistic case 27 , derived by replacing the vector current j µ with the relativistic charge current j µ ≡Ψ(x) γ µ Ψ(x) (where now Ψ(x) are spinors and γ µ are the Dirac γ-matrices).…”